{"title":"数学物理边值问题的双场拉格朗日乘子弱解","authors":"Mariana Chivu Cojocaru, A. Matei","doi":"10.3846/mma.2022.15827","DOIUrl":null,"url":null,"abstract":"A new variational approach for a boundary value problem in mathematical physics is proposed. By considering two-field Lagrange multipliers, we deliver a variational formulation consisting of a mixed variational problem which is equivalent with a saddle point problem. Thus, the unique solvability of the weak formulation we propose is governed by the saddle point theory. Alternative variational formulations and some of their connections are also discussed.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":"126 1","pages":"561-572"},"PeriodicalIF":1.6000,"publicationDate":"2022-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Weak solutions via two-field Lagrange Multipliers for boundary Value Problems in Mathematical Physics\",\"authors\":\"Mariana Chivu Cojocaru, A. Matei\",\"doi\":\"10.3846/mma.2022.15827\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A new variational approach for a boundary value problem in mathematical physics is proposed. By considering two-field Lagrange multipliers, we deliver a variational formulation consisting of a mixed variational problem which is equivalent with a saddle point problem. Thus, the unique solvability of the weak formulation we propose is governed by the saddle point theory. Alternative variational formulations and some of their connections are also discussed.\",\"PeriodicalId\":49861,\"journal\":{\"name\":\"Mathematical Modelling and Analysis\",\"volume\":\"126 1\",\"pages\":\"561-572\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2022-11-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Modelling and Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3846/mma.2022.15827\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Modelling and Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3846/mma.2022.15827","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Weak solutions via two-field Lagrange Multipliers for boundary Value Problems in Mathematical Physics
A new variational approach for a boundary value problem in mathematical physics is proposed. By considering two-field Lagrange multipliers, we deliver a variational formulation consisting of a mixed variational problem which is equivalent with a saddle point problem. Thus, the unique solvability of the weak formulation we propose is governed by the saddle point theory. Alternative variational formulations and some of their connections are also discussed.
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